#7 6. Where are the following functions discontinuous?x+2a) f(x) = TeE PCW =/x+2/x+0 x+0+ disconhnuous@Ob) f(x) =x2-x- discontinuouS @x-1&@x= |x2-1blc (x-) got cancelled out +P)-x(x-1)x < 31lcx? + 13, x 2 3)7. For what value(s) of c is f(x) = {4-x°,%3Dcontinuous everywhere?Page 2 of 3

Answered: blc (x-) got cancelled out »PW-x(x-1)…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

See similar textbooks

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
At what x-value is the global minimum for f(x)=x2−4x+3 within the interval 0≤x≤5?
If (5,2) is a critical point for the function y= f(x) and f''(x) is + , what can we conclude regarding the point (5,2)?
The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells in the blood. If S = k(H) = aHe-bH for positive constants a and b, with domain (0, infinity) and k'(H) = ae-bH(1-bH) 1. Use the definition to find the only critical point H1 of k on its domain. 2. Use a number line and the first derivative test to show that the oxygen supply is maximised at H1.You have to explain how you determine the sign of the first derivative on every interval. 3. What is the maximum oxygen supply? 4. How does increasing the value of the constants a and b in the same proportion change the maximumvalue of S? Please answer 3 and 4
The function y = 1/x does not take on either a maximum or a minimum on the interval 0 < x < 1 even though the function is continuous on this interval. Does this contradict the Extreme Value Theorem for continuous functions? Why?
11. Let h(x) = x^4 − 2x^2 + 3.(a) Find all critical points and use the First Derivative Test to characterize each as a local maximum, local minimum, or neither.(b) Use the Second Derivative Test to check your answers.(c) Find all inflection points.
Suppose g(x) is a differentiable function such that g′(3) = 0 and g′′(3) = 0. Then the Second Derivative Test guarantees that x = 3 is neither a local maximum nor a local minimum. Explain why
(i) Discuss the continuity of the function f(x) = {x2 − 3x if x < 2 2x + 4 if x ≥ 2ontheopeninterval0< x<2andontheclosedinterval0≤x≤2.(ii) Anefficiencystudyofthemorningshiftatacertainfactoryindicatesthatanaverage worker arriving on the job at 7: 00 A. M. will have assembled f (x) = x3 + 6x2 + 15x units x hours later. Approximately how many units will the worker assemble between8:00and8:15A.M.?(iii) A manufacturer’s total cost is C(q) = 0.1q3 + 0.5q2 + 500q + 200dollars when the level of production is q units.The current level of production is 4 units, and the manufacturer is planning to increase this to 4.1 units. Estimate how the total cost will change as a result.
3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a) Find f"(x). (b) Then use the second derivative test to identify the critical point as eithera local minimum, a local maximum, or neither.

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

College Algebra

Algebra

ISBN:

9781938168383

Author:

Jay Abramson

Publisher:

OpenStax

SEE MORE TEXTBOOKS

blc (x-) got cancelled out »PW-x(x-1) (x+) 7. For what value(s) of c is f(x) = 4- x°, cr2 + 13 x < 31 %3D